A222007 a(n+1) is the smallest prime factor of any (Product_{k=1..j} a(k)) + (Product_{k=j+1..n} a(k)) for j=0..n.

2, 3, 5, 11, 41, 7, 23, 17, 19, 13, 37, 53, 73, 151, 29, 43, 31, 59, 71, 47, 79, 61, 107, 83, 103, 163, 109, 89, 101, 113, 67, 97, 137, 131, 139, 127, 229, 149, 173, 227, 179, 239, 181, 191, 193, 167, 197, 241, 277, 157, 233, 211, 397, 257, 271, 283, 251, 281, 313, 269, 347, 349, 317, 263, 379, 223, 367, 199, 353, 401, 421, 463, 293, 337, 383, 389, 331, 431, 359, 443

Offset

1,1

Links

Table of n, a(n) for n=1..80.

Example

For n=4, a = <2,3,5>, yielding sums <1+2*3*5, 2+3*5, 2*3+5, 2*3*5+1> = <31,17,11,31>, with least prime factor a(4)=11.

Prog

(PARI) prodsum(ls) = local(left=1, right=prod(x=1, #ls, ls[x]), o=vector(#ls)); for(x=1, #ls, left*=ls[x]; right/=ls[x]; o[x]=left+right); o
newlpf(v) = local(l=0, fs); for(x=1, #v, fs=factor(v[x], if(l>500000, 0, l)); if(!l||fs[1, 1]<l, l=fs[1, 1])); l
s=[2]; while(#s<80, s=concat(s, [newlpf(prodsum(s))]))

Crossrefs

A modification of A000945, the Euclid-Mullin sequence, which looks only at factors from the j=n term.

Sequence in context: A127181 A323611 A113734 * A188142 A276531 A276532

Adjacent sequences: A222004 A222005 A222006 * A222008 A222009 A222010

Keyword

nonn,easy

Author

Phil Carmody, Feb 23 2013

Status

approved